Compactness for omitting of types
نویسندگان
چکیده
منابع مشابه
Omitting types for infinitary [0,1]-valued logic
We describe an infinitary logic for metric structures which is analogous to Lω1,ω . We show that this logic is capable of expressing several concepts from analysis that cannot be expressed in finitary continuous logic. Using topological methods, we prove an omitting types theorem for countable fragments of our infinitary logic. We use omitting types to prove a two-cardinal theorem, which yields...
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The model theory of metric structures ([?]) was successfully applied to analyze ultrapowers of C*-algebras in [?] and [?]. Since important classes of separable C*-algebras, such as UHF, AF, or nuclear algebras, are not elementary (i.e., not characterized by their theory—see [?, §6.1]), for a moment it seemed that model theoretic methods do not apply to these classes of C*-algebras. We prove res...
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An omitting types theorem for countable models of superstable theories containing an infinite set of indiscernibles is proved. Various corollaries and applications are given. 1. One of the most useful ways that the model theorist has for controlling models is to attempt to specify the element types that models realize and omit. In this paper we present an omitting types theorem which seems well...
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We show that the class of 1-exact operator systems is not uniformly definable by a sequence of types. We use this fact to show that there is no finitary version of Arveson’s extension theorem. Next, we show that WEP is equivalent to a certain notion of existential closedness for C∗-algebras and use this equivalence to give a simpler proof of Kavruk’s result that WEP is equivalent to the complet...
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The omitting types theorem of infinitary logic is used to prove that every small II set of analysis or any small 2. set of set theory is constructible. In what follows we could use either the omitting types theorem for infinitary logic or the same theorem for what Grilliot[2] calls (eA)-logic. I find the latter more appealing. Suppose i_ is a finitary logical language containing the symbols of ...
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ژورنال
عنوان ژورنال: Annals of Mathematical Logic
سال: 1978
ISSN: 0003-4843
DOI: 10.1016/0003-4843(78)90007-4